Calculating the Radius of a Hill for Weightless Sensation at 42 mph

In summary, the conversation discusses the concept of feeling weightless while traveling at a certain speed over a smooth, rounded hill. The question of what equation to use is raised, and it is suggested to assume the hill is circular. The discussion then delves into the forces at play during circular motion and how to solve for the radius of the hill.
  • #1
Hafsaaa
7
0

Homework Statement



It is found (through and error) that you will "feel" weightless when you travela round at 42 mph over a smoothy rounded hill. What is the radius of the hill?


Homework Equations



I'm not sure what equation to use with this problem

The Attempt at a Solution


the only thing I know is the answer, which is 35.6 m.
Could someone help walk through this problem? It would be much appreciated.
 
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  • #2
Hafsaaa said:

The Attempt at a Solution


the only thing I know is the answer, which is 35.6 m.
Could someone help walk through this problem? It would be much appreciated.

You'll need to assume the hill is circular, so if you feel weightless, how does this relate to your actual weight with respect to the normal reaction. For circular motion what sort of force would keep you moving in a circle?
 
  • #3
rock.freak667 said:
You'll need to assume the hill is circular, so if you feel weightless, how does this relate to your actual weight with respect to the normal reaction. For circular motion what sort of force would keep you moving in a circle?

Well since I'm moving in a verticle circle would gravity be force acting on me?
 
  • #4
Hafsaaa said:
Well since I'm moving in a verticle circle would gravity be force acting on me?

There would be the normal reaction and your weight. If you are weightless then what is the normal reaction equal to?
 
  • #5
rock.freak667 said:
There would be the normal reaction and your weight. If you are weightless then what is the normal reaction equal to?

it would be zero correct?
 
  • #6
Hafsaaa said:
it would be zero correct?

Right, so that means only the weight is providing the centripetal force. So equate the two and solve for r.
 

1. What is the unknown radius of a hill?

The unknown radius of a hill refers to the distance from the center of the hill to its outer edge or perimeter. It is a measurement that is often used in geology and geography to describe the size and shape of a hill.

2. Why is the radius of a hill important to know?

The radius of a hill is an important measurement because it can provide valuable information about the size, shape, and slope of the hill. It can also help in determining the amount of surface area and volume of the hill, which can be useful in various scientific studies and calculations.

3. How is the radius of a hill measured?

The radius of a hill can be measured using various methods, such as using a handheld measuring tool like a ruler or tape measure, or through more advanced techniques like remote sensing and aerial photography. The specific method used will depend on the size and location of the hill.

4. Can the radius of a hill change over time?

Yes, the radius of a hill can change over time due to various natural processes, such as erosion, weathering, and tectonic movements. Human activities, such as construction and mining, can also alter the shape and size of a hill and therefore affect its radius.

5. How does the radius of a hill relate to its overall topography?

The radius of a hill is an important aspect of its topography, as it can influence the overall shape and form of the hill. For example, a hill with a larger radius will have a gentler slope and a broader summit, while a hill with a smaller radius will have a steeper slope and a more pointed summit.

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